Question

What values for theta (0≤theta≤2π) cos theta- tan theta cos theta=0?

Answer 1

`\theta = (\pi)/(2) ,(3\pi)/(2),(\pi)/(4) , (5\pi)/(4)`

Step-by-step explanation

We want to solve the equation;

`\cos( \theta) - \tan( \theta) \cos( \theta) = 0`

We factor to get:

`\cos\theta(1 - \tan\theta) = 0`

Either

`\cos\theta = 0`

Or

`1 - \tan \theta = 0`

For

`\cos\theta = 0`

We gave

`\theta = (\pi)/(2) ,(3\pi)/(2)`

When

`\tan \theta = 1`

Then,

`\theta = (\pi)/(4) , (5\pi)/(4)`

Therefore the solution on the interval

`0 \leqslant \theta \: \leqslant 2\pi`

is

`\theta = (\pi)/(2) ,(3\pi)/(2),(\pi)/(4) , (5\pi)/(4)`